A rear-projection image display device uses a transmissive screen for displaying image light that has been enlarged and projected onto the screen from the back. JP 2000-292864A discloses a transmissive screen comprising a linear Fresnel lens sheet for deflecting image light rays, which have been enlarged and projected by a light source, to make them approximately parallel to each other, and a diffusion sheet for diffusing image light that has exited the linear Fresnel lens sheet, thereby increasing the viewing angle.
The linear Fresnel lens sheet has a number of lens surfaces arranged in a certain arrangement direction and, owing to the combination of the lens surfaces, exerts a certain optical effect on incident light. In a typical linear Fresnel lens sheet, the inclination angle of a lens surface with respect to the sheet plane increases with the distance of the lens surface from the middle of the sheet in the arrangement direction of the lens surfaces. Such a linear Fresnel lens sheet is generally produced by a method comprising supplying a UV curable resin between a roll-shaped mold and a substrate which is being fed along the circumference of the roll-shaped mold, and irradiating the resin with ultraviolet light. The use of a roll-shaped mold can produce a linear Fresnel lens sheet with high production efficiency. Further, linear Fresnel lens sheets, produced by such a method, are expected to be used in a variety of applications.
To produce a linear Fresnel lens sheet by the above-described method, it is necessary to prepare a roll-shaped mold. A method for producing a roll-shaped mold will now be described with reference to FIGS. 14 through 16. FIGS. 14(a) through 14(c) are schematic views illustrating a method for producing a roll-shaped mold, FIG. 15 is a schematic view illustrating a method for machining a middle portion of the roll-shaped mold, and FIG. 16 is a schematic enlarged view illustrating a middle portion of the machined roll-shaped mold.
First, as shown in FIG. 14(a), a substrate roller 503 made of a metal is prepared, and surface smoothing of the substrate roller 503 is performed with a turning tool 501. Next, as shown in FIG. 14(b), a first annular groove group 510, consisting of a number of first annular grooves 511, is formed sequentially from one end toward the middle of the roll-shaped mold 500 (substrate roller 503) in the axial direction r. Each first annular groove 511 has a first inclined surface 512 for the production of a lens surface. The inclination angle γ of a first inclined surface 512 with respect to the axial direction r increases with the distance of the first inclined surface 512 from the middle of the roll-shaped mold 500 in the axial direction r. Thus, the cutting angle β of the turning tool 501 with respect to the axial direction r is made smaller for a first inclined surface 512 than for the adjacent first inclined surface 512 lying farther from the middle of the roll-shaped mold 500 in the axial direction r. In particular, the substrate roller 503 is machined by moving the turning tool 501 in the radial direction n while keeping the cutting edge of the turning tool 501 at a predetermined cutting angle β with respect to the axial direction r, thereby forming a first annular groove 511. The turning tool 501 is then retreated. Next, after moving the turning tool 501 in the axial direction r, the cutting angle β of the turning tool 501 is changed to smaller, and machining of the next first annular groove 511 is performed. However, as shown in FIG. 15, if the cutting angle β of the turning tool 501 is made smaller in a middle portion of the substrate roller 503, then the turning tool 501 will make contact with a previously-machined first annular groove 511. Therefore, a first annular groove 511 is formed while maintaining the same cutting angle β in the middle portion of the substrate roller 503. Thus, in the middle portion of the substrate roller 503, it becomes physically difficult to perform machining of a first annular groove 511 at a designed cutting angle β; a need arises to perform machining of a first annular groove 511 at a cutting angle which is larger than the designed cutting angle.
After forming the first annular groove group 510, the turning tool 501 is replaced with a new one. Thereafter, as shown in FIG. 14(c), a second annular groove group 520 is formed sequentially from the middle toward the other end of the roll-shaped mold 500 in the axial direction r in the same manner as in the formation of the first annular groove group 510. The second annular groove group 520 consists of a number of second annular grooves 521 each having a second inclined surface 522 for the production of a lens surface.
At the boundary between the first annular groove group 510 and the second annular groove group 520, it is difficult to smoothly connect the first inclined surface 512 of the first annular groove 511 and the second inclined surface 522 of the second annular groove 521 because of a number of factors such as the accuracy of positioning (positioning accuracy upon turning) of the cutting angle β of the turning tool 501, the accuracy of mounting of the turning tool 501 upon replacement, the accuracy of feeding of the turning tool 501 by means of a lathe, backlash, etc. Therefore, as shown in FIG. 16, a stepped joint 502 is formed between the first inclined surface 512 and the second inclined surface 522 whose inclination angles with respect to the radial direction n are symmetrical.
FIG. 17 shows a linear Fresnel lens sheet shaped by the use of the roll-shaped mold 500 produced by the above-described method. As shown in FIG. 17, the linear Fresnel lens sheet includes a first lens surface group 410 consisting of a number of first lens surfaces 411 which are inclined toward one side from the normal direction N to the sheet plane of the linear Fresnel lens sheet, and a second lens surface group 420 consisting of a number of second lens surfaces 421 which are inclined toward the opposite side from the normal direction N. As described above, machining is performed in a middle portion of the roll-shaped mold 500 at a cutting angle which is larger than a desired cutting angle. Accordingly, in a middle portion of the linear Fresnel lens sheet, the lens angle α, which is the inclination angle of each lens surface 411 or 421 with respect to the sheet plane of the linear Fresnel lens sheet, is larger than a desired inclination angle. Further, at the boundary between the first lens surface group 410 and the second lens surface group 420, i.e. at the position corresponding to the joint 502 formed between those inclined surfaces of the roll-shaped mold 500 whose inclination angles with respect to the radial direction n are symmetrical, a navel 402 is defined between those lens surfaces 411, 421 whose inclination angles with respect to the normal direction N are symmetrical.
Consider the case where light, mainly comprising parallel light rays, enters the linear Fresnel lens sheet shown in FIG. 17. Light mainly comprising parallel light rays is concentrated into a predetermined light-concentrated area (focus area in the illustrated case) by the lens effect of the linear Fresnel lens sheet. However, because the lens angle α of a lens surface with respect to the sheet plane 1a is larger than a desired inclination angle in a middle portion of the linear Fresnel lens sheet, light entering the middle portion will not be refracted at a desired refraction angle and will not be concentrated into the predetermined light-concentrated area. Therefore, the middle portion of the linear Fresnel lens sheet appears dark to a viewer viewing light that has been concentrated into the light-concentrated area.
Further, in the case where only a transmissive screen exists between the linear Fresnel lens sheet and a viewer, the viewer can view the linear Fresnel lens sheet itself depending on the viewing angle of the viewer. In that case, the navel of the linear Fresnel lens sheet is clearly visible to the viewer. This deteriorates the quality of images displayed on the screen.
Recently attempts have been made to reduce the distance between a light source and a transmissive screen so as to construct a compact rear-projection image display device. However, it has been found through the present inventors' studies that when the distance between a light source and a transmissive screen is short, a stripe pattern, consisting of bright and dark stripes extending in a direction perpendicular to the arrangement direction of lens surfaces, may appear on the transmissive screen when the screen is viewed in a particular direction. FIG. 18 schematically shows a stripe pattern which can appear on the light exit-side surface 602a of a conventional transmissive screen 602. As shown in FIG. 18, the stripe pattern appears in an area S remote from the middle of the light exit-side surface 602a. 